Acoustic waves may be used to characterize surface and bulk properties of materials, including film thickness in layered materials, material stiffness (elastic modulus), and sound velocity. Photoacoustic methods have been applied to the characterization of mesoscopic structures (which may have properties that differ from their bulk counterparts) and to the nondestructive, non-contact probing of subsurface structural elements and defects in opaque materials. Applications of photoacoustic spectroscopy are described, for example, in “Picosecond acoustic phonon pulse generation in nickel and chromium,” Physical Review B 67, 205421 (2003) by T. Saito, O. Matsuda and O. B. Wright, and in “Transient grating measurements of film thickness in multilayer metal films,” Journal of Applied Physics 90, 4392-4402 (2001) by R. M. Slayton, K. A. Nelson and A. A. Maznev, the contents of both of which are incorporated herein by reference.
Time-resolved sample characterization using acoustic waves is initiated in some cases by first generating an acoustic wave at the surface of a sample through absorption of an incident optical waveform. Absorption may lead to the generation of surface acoustic waves that propagate along the material surface, or in thin layers at or near the surface. Absorption may also lead to the generation of acoustic waves, such as longitudinal waves, that propagate into the bulk of the sample. Acoustic waves may also be introduced into the bulk region of the sample through direct absorption of an incident waveform in the bulk region.
In some cases, in order to generate acoustic waves through absorption at or near a surface, one or more optical pulses are employed. The pulses are short in duration relative to the inverse of the acoustic frequency of interest, and are at a wavelength that is strongly absorbed at the surface of the material through which the acoustic wave propagates. Absorption of a short-duration optical pulse by a sample heats the sample and launches an acoustic pulse, which may be thought of as an acoustic wavepacket. Such a wavepacket may include, for example, from one-half to one complete acoustic cycle. Consequently, the wavepacket may include a broad distribution of acoustic frequency and wavevector components. Broadband acoustic wavepackets with frequency components up to about 500 GHz may be generated, for example, through optical irradiation of a thin aluminum film by a subpicosecond laser pulse.
Broadband acoustic pulses may be used to study the structure of material samples. Partial reflections of a broadband acoustic waveform occur at external and, if present, internal sample interfaces, and are due to the acoustic impedance mismatch of the materials which form the interface. The partial reflections may be detected as “echoes” at a sample external surface. For example, detection of acoustic waveforms reaching the surface of the sample may involve the time-resolved measurement of strain-induced changes in reflectivity of a transducer layer on the surface of the sample. The response of a sample to a broadband acoustic waveform may alternatively be detected by coherent scattering of a measurement pulse, or by interferometry. Transformation of a time-resolved sample measurement signal to the frequency domain may permit the study of one or more frequency-dependent properties of the sample. At very high acoustic frequencies, the sensitivity of broadband acoustic methods may be limited by the signal-to-noise ratio of the measurement data, and by the ease with which unambiguous frequency-dependent sound velocities, damping rates, and other sample parameters may be extracted from the measurement data.
Narrowband acoustic measurements, in contrast to broadband measurements, may be employed to determine the acoustic velocity, damping rate, and/or other properties of a sample at, nominally, one or more specific acoustic measurement frequencies. The signal-to-noise ratio of narrowband measurements may be relatively high, since all of the acoustic energy is concentrated in a narrow frequency band. High acoustic frequencies are of particular interest, since they provide greater resolution in photoacoustic spectroscopy. When the frequency ω of a narrowband acoustic pulse, propagating at velocity νs within a sample, is tuned such that the inverse of the frequency corresponds to a characteristic relaxation time τc of the sample (τcω˜1), the acoustic velocity and attenuation rate change in a manner which yields structural and other information about the sample. A similar condition holds if the inverse of the acoustic wavevector q=ω/νs approaches the order of a structural element of size d (qd˜1). At higher frequencies, faster responses and smaller structural properties of a sample may be measured using narrowband acoustic waveforms.
Generation of tunable, narrowband acoustic pulses through optical means has long been possible at megahertz frequencies by employing techniques such as impulsive stimulated thermal scattering (ISTS). ISTS is described, for example, in “Laser-induced phonon spectroscopy. Optical generation of ultrasonic waves and investigation of electronic excited-state interactions in solids.” Physical Review B 24, 3261-3275 (1981) by K. A. Nelson, D. R. Lutz, M. D. Fayer and L. Madison, the contents of which are incorporated herein by reference. The ISTS technique generally includes spatially and temporally overlapping two laser pulses inside a sample, where they form an interference pattern with a spatial periodicity that depends on the angle at which they cross and on the optical wavelength of the pulses. Absorption of the pulses heats the sample, and concurrent rapid expansion launches counter-propagating acoustic waves with an acoustic wavelength that nominally matches the period of the laser interference pattern. Tuning of the acoustic wavelength may be achieved by changing the crossing angle of the two pulses. Acoustic waves with frequencies of tens of MHz to a few GHz may be produced in this manner, Measurement of material properties may be accomplished by monitoring the time-dependent refractive index of the sample. For example, refractive index changes may be monitored by measuring the coherent scattering of a third laser pulse.
Higher frequency, narrowband acoustic pulses at GHz frequencies have been generated using multiple quantum well materials with a specified spatial periodicity, and with materials containing metal films with specified thicknesses which utilize multiple internal reflections. For example, femtosecond optical irradiation of multiple quantum well structures is disclosed in “Control of Coherent Acoustic Phonons in Semiconductor Quantum Wells,” Physical Review Letters 86, 5604-5607 (2001) by Ü. Özgür, C.-W. Lee and H. O. Everitt, the contents of which are incorporated herein by reference. Acoustic waves at frequencies of about 700 GHz have been generated using this method. The spatial periodicity of the quantum wells determines the nominal frequency of the acoustic wave which is generated, and so a specific quantum well structure is employed to produce a particular acoustic frequency.
Thin metal film structures which have been used to generate narrowband acoustic waves at gigahertz frequencies are disclosed, for example, in “Phonon attenuation in amorphous solids studied by picosecond ultrasonics,” Physical Review B 54, 203-213 (1996) by C. J. Morath and H. J. Maris, the contents of which are incorporated herein by reference. The structures may include a metal transducer layer deposited onto the surface of a sample of interest. Irradiation of the transducer layer generates a propagating acoustic wave therein. Each time the acoustic wave encounters the interface between the transducer layer and the sample, a portion of the acoustic wave intensity is transmitted through the interface and enters the sample. For every round trip the acoustic wave completes inside the transducer layer, partial transmission into the sample yields an additional “cycle” of a narrowband acoustic waveform. Acoustic waves with frequencies greater than 300 GHz may be generated using this method. Since the acoustic frequency depends upon the metal transducer thickness and sound velocity, a different transducer is used to produce each acoustic frequency of interest.
Measurement of at least one of the intensity, phase, temporal location, frequency spectrum and/or spatial position of a measurement beam following interaction with a sample in which an acoustic wave is propagating yields information which may be used to characterize one or more properties of the sample. For example, measurements of the times-of-flight of an acoustic wave and its partial reflections from sample interfaces may be used to determine the thicknesses of one or more layers comprising the sample. Phase shifts of the measured time-dependent surface displacement for two different known sample thicknesses may be determined in order to calculate the sound velocity at a particular frequency in the sample. The time-dependent intensity of the sample response may be used to determine the acoustic damping rate at a particular frequency. Further, all such measurements may be performed in a manner which is nondestructive to the sample and which involves no sample contact.